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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.filter;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.NullArgumentException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.linear.Array2DRowRealMatrix;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.linear.ArrayRealVector;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.linear.CholeskyDecomposition;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.linear.DecompositionSolver;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.linear.MatrixDimensionMismatchException;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.linear.MatrixUtils;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.linear.NonSquareMatrixException;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.linear.RealMatrix;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.linear.RealVector;<a name="line.29"></a>
<FONT color="green">030</FONT>    import org.apache.commons.math3.linear.SingularMatrixException;<a name="line.30"></a>
<FONT color="green">031</FONT>    import org.apache.commons.math3.util.MathUtils;<a name="line.31"></a>
<FONT color="green">032</FONT>    <a name="line.32"></a>
<FONT color="green">033</FONT>    /**<a name="line.33"></a>
<FONT color="green">034</FONT>     * Implementation of a Kalman filter to estimate the state &lt;i&gt;x&lt;sub&gt;k&lt;/sub&gt;&lt;/i&gt;<a name="line.34"></a>
<FONT color="green">035</FONT>     * of a discrete-time controlled process that is governed by the linear<a name="line.35"></a>
<FONT color="green">036</FONT>     * stochastic difference equation:<a name="line.36"></a>
<FONT color="green">037</FONT>     *<a name="line.37"></a>
<FONT color="green">038</FONT>     * &lt;pre&gt;<a name="line.38"></a>
<FONT color="green">039</FONT>     * &lt;i&gt;x&lt;sub&gt;k&lt;/sub&gt;&lt;/i&gt; = &lt;b&gt;A&lt;/b&gt;&lt;i&gt;x&lt;sub&gt;k-1&lt;/sub&gt;&lt;/i&gt; + &lt;b&gt;B&lt;/b&gt;&lt;i&gt;u&lt;sub&gt;k-1&lt;/sub&gt;&lt;/i&gt; + &lt;i&gt;w&lt;sub&gt;k-1&lt;/sub&gt;&lt;/i&gt;<a name="line.39"></a>
<FONT color="green">040</FONT>     * &lt;/pre&gt;<a name="line.40"></a>
<FONT color="green">041</FONT>     *<a name="line.41"></a>
<FONT color="green">042</FONT>     * with a measurement &lt;i&gt;x&lt;sub&gt;k&lt;/sub&gt;&lt;/i&gt; that is<a name="line.42"></a>
<FONT color="green">043</FONT>     *<a name="line.43"></a>
<FONT color="green">044</FONT>     * &lt;pre&gt;<a name="line.44"></a>
<FONT color="green">045</FONT>     * &lt;i&gt;z&lt;sub&gt;k&lt;/sub&gt;&lt;/i&gt; = &lt;b&gt;H&lt;/b&gt;&lt;i&gt;x&lt;sub&gt;k&lt;/sub&gt;&lt;/i&gt; + &lt;i&gt;v&lt;sub&gt;k&lt;/sub&gt;&lt;/i&gt;.<a name="line.45"></a>
<FONT color="green">046</FONT>     * &lt;/pre&gt;<a name="line.46"></a>
<FONT color="green">047</FONT>     *<a name="line.47"></a>
<FONT color="green">048</FONT>     * &lt;p&gt;<a name="line.48"></a>
<FONT color="green">049</FONT>     * The random variables &lt;i&gt;w&lt;sub&gt;k&lt;/sub&gt;&lt;/i&gt; and &lt;i&gt;v&lt;sub&gt;k&lt;/sub&gt;&lt;/i&gt; represent<a name="line.49"></a>
<FONT color="green">050</FONT>     * the process and measurement noise and are assumed to be independent of each<a name="line.50"></a>
<FONT color="green">051</FONT>     * other and distributed with normal probability (white noise).<a name="line.51"></a>
<FONT color="green">052</FONT>     * &lt;p&gt;<a name="line.52"></a>
<FONT color="green">053</FONT>     * The Kalman filter cycle involves the following steps:<a name="line.53"></a>
<FONT color="green">054</FONT>     * &lt;ol&gt;<a name="line.54"></a>
<FONT color="green">055</FONT>     * &lt;li&gt;predict: project the current state estimate ahead in time&lt;/li&gt;<a name="line.55"></a>
<FONT color="green">056</FONT>     * &lt;li&gt;correct: adjust the projected estimate by an actual measurement&lt;/li&gt;<a name="line.56"></a>
<FONT color="green">057</FONT>     * &lt;/ol&gt;<a name="line.57"></a>
<FONT color="green">058</FONT>     * &lt;p&gt;<a name="line.58"></a>
<FONT color="green">059</FONT>     * The Kalman filter is initialized with a {@link ProcessModel} and a<a name="line.59"></a>
<FONT color="green">060</FONT>     * {@link MeasurementModel}, which contain the corresponding transformation and<a name="line.60"></a>
<FONT color="green">061</FONT>     * noise covariance matrices. The parameter names used in the respective models<a name="line.61"></a>
<FONT color="green">062</FONT>     * correspond to the following names commonly used in the mathematical<a name="line.62"></a>
<FONT color="green">063</FONT>     * literature:<a name="line.63"></a>
<FONT color="green">064</FONT>     * &lt;ul&gt;<a name="line.64"></a>
<FONT color="green">065</FONT>     * &lt;li&gt;A - state transition matrix&lt;/li&gt;<a name="line.65"></a>
<FONT color="green">066</FONT>     * &lt;li&gt;B - control input matrix&lt;/li&gt;<a name="line.66"></a>
<FONT color="green">067</FONT>     * &lt;li&gt;H - measurement matrix&lt;/li&gt;<a name="line.67"></a>
<FONT color="green">068</FONT>     * &lt;li&gt;Q - process noise covariance matrix&lt;/li&gt;<a name="line.68"></a>
<FONT color="green">069</FONT>     * &lt;li&gt;R - measurement noise covariance matrix&lt;/li&gt;<a name="line.69"></a>
<FONT color="green">070</FONT>     * &lt;li&gt;P - error covariance matrix&lt;/li&gt;<a name="line.70"></a>
<FONT color="green">071</FONT>     * &lt;/ul&gt;<a name="line.71"></a>
<FONT color="green">072</FONT>     *<a name="line.72"></a>
<FONT color="green">073</FONT>     * @see &lt;a href="http://www.cs.unc.edu/~welch/kalman/"&gt;Kalman filter<a name="line.73"></a>
<FONT color="green">074</FONT>     *      resources&lt;/a&gt;<a name="line.74"></a>
<FONT color="green">075</FONT>     * @see &lt;a href="http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf"&gt;An<a name="line.75"></a>
<FONT color="green">076</FONT>     *      introduction to the Kalman filter by Greg Welch and Gary Bishop&lt;/a&gt;<a name="line.76"></a>
<FONT color="green">077</FONT>     * @see &lt;a href="http://academic.csuohio.edu/simond/courses/eec644/kalman.pdf"&gt;<a name="line.77"></a>
<FONT color="green">078</FONT>     *      Kalman filter example by Dan Simon&lt;/a&gt;<a name="line.78"></a>
<FONT color="green">079</FONT>     * @see ProcessModel<a name="line.79"></a>
<FONT color="green">080</FONT>     * @see MeasurementModel<a name="line.80"></a>
<FONT color="green">081</FONT>     * @since 3.0<a name="line.81"></a>
<FONT color="green">082</FONT>     * @version $Id: KalmanFilter.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.82"></a>
<FONT color="green">083</FONT>     */<a name="line.83"></a>
<FONT color="green">084</FONT>    public class KalmanFilter {<a name="line.84"></a>
<FONT color="green">085</FONT>        /** The process model used by this filter instance. */<a name="line.85"></a>
<FONT color="green">086</FONT>        private final ProcessModel processModel;<a name="line.86"></a>
<FONT color="green">087</FONT>        /** The measurement model used by this filter instance. */<a name="line.87"></a>
<FONT color="green">088</FONT>        private final MeasurementModel measurementModel;<a name="line.88"></a>
<FONT color="green">089</FONT>        /** The transition matrix, equivalent to A. */<a name="line.89"></a>
<FONT color="green">090</FONT>        private RealMatrix transitionMatrix;<a name="line.90"></a>
<FONT color="green">091</FONT>        /** The transposed transition matrix. */<a name="line.91"></a>
<FONT color="green">092</FONT>        private RealMatrix transitionMatrixT;<a name="line.92"></a>
<FONT color="green">093</FONT>        /** The control matrix, equivalent to B. */<a name="line.93"></a>
<FONT color="green">094</FONT>        private RealMatrix controlMatrix;<a name="line.94"></a>
<FONT color="green">095</FONT>        /** The measurement matrix, equivalent to H. */<a name="line.95"></a>
<FONT color="green">096</FONT>        private RealMatrix measurementMatrix;<a name="line.96"></a>
<FONT color="green">097</FONT>        /** The transposed measurement matrix. */<a name="line.97"></a>
<FONT color="green">098</FONT>        private RealMatrix measurementMatrixT;<a name="line.98"></a>
<FONT color="green">099</FONT>        /** The internal state estimation vector, equivalent to x hat. */<a name="line.99"></a>
<FONT color="green">100</FONT>        private RealVector stateEstimation;<a name="line.100"></a>
<FONT color="green">101</FONT>        /** The error covariance matrix, equivalent to P. */<a name="line.101"></a>
<FONT color="green">102</FONT>        private RealMatrix errorCovariance;<a name="line.102"></a>
<FONT color="green">103</FONT>    <a name="line.103"></a>
<FONT color="green">104</FONT>        /**<a name="line.104"></a>
<FONT color="green">105</FONT>         * Creates a new Kalman filter with the given process and measurement models.<a name="line.105"></a>
<FONT color="green">106</FONT>         *<a name="line.106"></a>
<FONT color="green">107</FONT>         * @param process<a name="line.107"></a>
<FONT color="green">108</FONT>         *            the model defining the underlying process dynamics<a name="line.108"></a>
<FONT color="green">109</FONT>         * @param measurement<a name="line.109"></a>
<FONT color="green">110</FONT>         *            the model defining the given measurement characteristics<a name="line.110"></a>
<FONT color="green">111</FONT>         * @throws NullArgumentException<a name="line.111"></a>
<FONT color="green">112</FONT>         *             if any of the given inputs is null (except for the control matrix)<a name="line.112"></a>
<FONT color="green">113</FONT>         * @throws NonSquareMatrixException<a name="line.113"></a>
<FONT color="green">114</FONT>         *             if the transition matrix is non square<a name="line.114"></a>
<FONT color="green">115</FONT>         * @throws DimensionMismatchException<a name="line.115"></a>
<FONT color="green">116</FONT>         *             if the column dimension of the transition matrix does not match the dimension of the<a name="line.116"></a>
<FONT color="green">117</FONT>         *             initial state estimation vector<a name="line.117"></a>
<FONT color="green">118</FONT>         * @throws MatrixDimensionMismatchException<a name="line.118"></a>
<FONT color="green">119</FONT>         *             if the matrix dimensions do not fit together<a name="line.119"></a>
<FONT color="green">120</FONT>         */<a name="line.120"></a>
<FONT color="green">121</FONT>        public KalmanFilter(final ProcessModel process, final MeasurementModel measurement)<a name="line.121"></a>
<FONT color="green">122</FONT>                throws NullArgumentException, NonSquareMatrixException, DimensionMismatchException,<a name="line.122"></a>
<FONT color="green">123</FONT>                       MatrixDimensionMismatchException {<a name="line.123"></a>
<FONT color="green">124</FONT>    <a name="line.124"></a>
<FONT color="green">125</FONT>            MathUtils.checkNotNull(process);<a name="line.125"></a>
<FONT color="green">126</FONT>            MathUtils.checkNotNull(measurement);<a name="line.126"></a>
<FONT color="green">127</FONT>    <a name="line.127"></a>
<FONT color="green">128</FONT>            this.processModel = process;<a name="line.128"></a>
<FONT color="green">129</FONT>            this.measurementModel = measurement;<a name="line.129"></a>
<FONT color="green">130</FONT>    <a name="line.130"></a>
<FONT color="green">131</FONT>            transitionMatrix = processModel.getStateTransitionMatrix();<a name="line.131"></a>
<FONT color="green">132</FONT>            MathUtils.checkNotNull(transitionMatrix);<a name="line.132"></a>
<FONT color="green">133</FONT>            transitionMatrixT = transitionMatrix.transpose();<a name="line.133"></a>
<FONT color="green">134</FONT>    <a name="line.134"></a>
<FONT color="green">135</FONT>            // create an empty matrix if no control matrix was given<a name="line.135"></a>
<FONT color="green">136</FONT>            if (processModel.getControlMatrix() == null) {<a name="line.136"></a>
<FONT color="green">137</FONT>                controlMatrix = new Array2DRowRealMatrix();<a name="line.137"></a>
<FONT color="green">138</FONT>            } else {<a name="line.138"></a>
<FONT color="green">139</FONT>                controlMatrix = processModel.getControlMatrix();<a name="line.139"></a>
<FONT color="green">140</FONT>            }<a name="line.140"></a>
<FONT color="green">141</FONT>    <a name="line.141"></a>
<FONT color="green">142</FONT>            measurementMatrix = measurementModel.getMeasurementMatrix();<a name="line.142"></a>
<FONT color="green">143</FONT>            MathUtils.checkNotNull(measurementMatrix);<a name="line.143"></a>
<FONT color="green">144</FONT>            measurementMatrixT = measurementMatrix.transpose();<a name="line.144"></a>
<FONT color="green">145</FONT>    <a name="line.145"></a>
<FONT color="green">146</FONT>            // check that the process and measurement noise matrices are not null<a name="line.146"></a>
<FONT color="green">147</FONT>            // they will be directly accessed from the model as they may change<a name="line.147"></a>
<FONT color="green">148</FONT>            // over time<a name="line.148"></a>
<FONT color="green">149</FONT>            RealMatrix processNoise = processModel.getProcessNoise();<a name="line.149"></a>
<FONT color="green">150</FONT>            MathUtils.checkNotNull(processNoise);<a name="line.150"></a>
<FONT color="green">151</FONT>            RealMatrix measNoise = measurementModel.getMeasurementNoise();<a name="line.151"></a>
<FONT color="green">152</FONT>            MathUtils.checkNotNull(measNoise);<a name="line.152"></a>
<FONT color="green">153</FONT>    <a name="line.153"></a>
<FONT color="green">154</FONT>            // set the initial state estimate to a zero vector if it is not<a name="line.154"></a>
<FONT color="green">155</FONT>            // available from the process model<a name="line.155"></a>
<FONT color="green">156</FONT>            if (processModel.getInitialStateEstimate() == null) {<a name="line.156"></a>
<FONT color="green">157</FONT>                stateEstimation = new ArrayRealVector(transitionMatrix.getColumnDimension());<a name="line.157"></a>
<FONT color="green">158</FONT>            } else {<a name="line.158"></a>
<FONT color="green">159</FONT>                stateEstimation = processModel.getInitialStateEstimate();<a name="line.159"></a>
<FONT color="green">160</FONT>            }<a name="line.160"></a>
<FONT color="green">161</FONT>    <a name="line.161"></a>
<FONT color="green">162</FONT>            if (transitionMatrix.getColumnDimension() != stateEstimation.getDimension()) {<a name="line.162"></a>
<FONT color="green">163</FONT>                throw new DimensionMismatchException(transitionMatrix.getColumnDimension(),<a name="line.163"></a>
<FONT color="green">164</FONT>                                                     stateEstimation.getDimension());<a name="line.164"></a>
<FONT color="green">165</FONT>            }<a name="line.165"></a>
<FONT color="green">166</FONT>    <a name="line.166"></a>
<FONT color="green">167</FONT>            // initialize the error covariance to the process noise if it is not<a name="line.167"></a>
<FONT color="green">168</FONT>            // available from the process model<a name="line.168"></a>
<FONT color="green">169</FONT>            if (processModel.getInitialErrorCovariance() == null) {<a name="line.169"></a>
<FONT color="green">170</FONT>                errorCovariance = processNoise.copy();<a name="line.170"></a>
<FONT color="green">171</FONT>            } else {<a name="line.171"></a>
<FONT color="green">172</FONT>                errorCovariance = processModel.getInitialErrorCovariance();<a name="line.172"></a>
<FONT color="green">173</FONT>            }<a name="line.173"></a>
<FONT color="green">174</FONT>    <a name="line.174"></a>
<FONT color="green">175</FONT>            // sanity checks, the control matrix B may be null<a name="line.175"></a>
<FONT color="green">176</FONT>    <a name="line.176"></a>
<FONT color="green">177</FONT>            // A must be a square matrix<a name="line.177"></a>
<FONT color="green">178</FONT>            if (!transitionMatrix.isSquare()) {<a name="line.178"></a>
<FONT color="green">179</FONT>                throw new NonSquareMatrixException(<a name="line.179"></a>
<FONT color="green">180</FONT>                        transitionMatrix.getRowDimension(),<a name="line.180"></a>
<FONT color="green">181</FONT>                        transitionMatrix.getColumnDimension());<a name="line.181"></a>
<FONT color="green">182</FONT>            }<a name="line.182"></a>
<FONT color="green">183</FONT>    <a name="line.183"></a>
<FONT color="green">184</FONT>            // row dimension of B must be equal to A<a name="line.184"></a>
<FONT color="green">185</FONT>            if (controlMatrix != null &amp;&amp;<a name="line.185"></a>
<FONT color="green">186</FONT>                controlMatrix.getRowDimension() &gt; 0 &amp;&amp;<a name="line.186"></a>
<FONT color="green">187</FONT>                controlMatrix.getColumnDimension() &gt; 0 &amp;&amp;<a name="line.187"></a>
<FONT color="green">188</FONT>                (controlMatrix.getRowDimension() != transitionMatrix.getRowDimension() ||<a name="line.188"></a>
<FONT color="green">189</FONT>                 controlMatrix.getColumnDimension() != 1)) {<a name="line.189"></a>
<FONT color="green">190</FONT>                throw new MatrixDimensionMismatchException(controlMatrix.getRowDimension(),<a name="line.190"></a>
<FONT color="green">191</FONT>                                                           controlMatrix.getColumnDimension(),<a name="line.191"></a>
<FONT color="green">192</FONT>                                                           transitionMatrix.getRowDimension(), 1);<a name="line.192"></a>
<FONT color="green">193</FONT>            }<a name="line.193"></a>
<FONT color="green">194</FONT>    <a name="line.194"></a>
<FONT color="green">195</FONT>            // Q must be equal to A<a name="line.195"></a>
<FONT color="green">196</FONT>            MatrixUtils.checkAdditionCompatible(transitionMatrix, processNoise);<a name="line.196"></a>
<FONT color="green">197</FONT>    <a name="line.197"></a>
<FONT color="green">198</FONT>            // column dimension of H must be equal to row dimension of A<a name="line.198"></a>
<FONT color="green">199</FONT>            if (measurementMatrix.getColumnDimension() != transitionMatrix.getRowDimension()) {<a name="line.199"></a>
<FONT color="green">200</FONT>                throw new MatrixDimensionMismatchException(measurementMatrix.getRowDimension(),<a name="line.200"></a>
<FONT color="green">201</FONT>                                                           measurementMatrix.getColumnDimension(),<a name="line.201"></a>
<FONT color="green">202</FONT>                                                           measurementMatrix.getRowDimension(),<a name="line.202"></a>
<FONT color="green">203</FONT>                                                           transitionMatrix.getRowDimension());<a name="line.203"></a>
<FONT color="green">204</FONT>            }<a name="line.204"></a>
<FONT color="green">205</FONT>    <a name="line.205"></a>
<FONT color="green">206</FONT>            // row dimension of R must be equal to row dimension of H<a name="line.206"></a>
<FONT color="green">207</FONT>            if (measNoise.getRowDimension() != measurementMatrix.getRowDimension() ||<a name="line.207"></a>
<FONT color="green">208</FONT>                measNoise.getColumnDimension() != 1) {<a name="line.208"></a>
<FONT color="green">209</FONT>                throw new MatrixDimensionMismatchException(measNoise.getRowDimension(),<a name="line.209"></a>
<FONT color="green">210</FONT>                                                           measNoise.getColumnDimension(),<a name="line.210"></a>
<FONT color="green">211</FONT>                                                           measurementMatrix.getRowDimension(), 1);<a name="line.211"></a>
<FONT color="green">212</FONT>            }<a name="line.212"></a>
<FONT color="green">213</FONT>        }<a name="line.213"></a>
<FONT color="green">214</FONT>    <a name="line.214"></a>
<FONT color="green">215</FONT>        /**<a name="line.215"></a>
<FONT color="green">216</FONT>         * Returns the dimension of the state estimation vector.<a name="line.216"></a>
<FONT color="green">217</FONT>         *<a name="line.217"></a>
<FONT color="green">218</FONT>         * @return the state dimension<a name="line.218"></a>
<FONT color="green">219</FONT>         */<a name="line.219"></a>
<FONT color="green">220</FONT>        public int getStateDimension() {<a name="line.220"></a>
<FONT color="green">221</FONT>            return stateEstimation.getDimension();<a name="line.221"></a>
<FONT color="green">222</FONT>        }<a name="line.222"></a>
<FONT color="green">223</FONT>    <a name="line.223"></a>
<FONT color="green">224</FONT>        /**<a name="line.224"></a>
<FONT color="green">225</FONT>         * Returns the dimension of the measurement vector.<a name="line.225"></a>
<FONT color="green">226</FONT>         *<a name="line.226"></a>
<FONT color="green">227</FONT>         * @return the measurement vector dimension<a name="line.227"></a>
<FONT color="green">228</FONT>         */<a name="line.228"></a>
<FONT color="green">229</FONT>        public int getMeasurementDimension() {<a name="line.229"></a>
<FONT color="green">230</FONT>            return measurementMatrix.getRowDimension();<a name="line.230"></a>
<FONT color="green">231</FONT>        }<a name="line.231"></a>
<FONT color="green">232</FONT>    <a name="line.232"></a>
<FONT color="green">233</FONT>        /**<a name="line.233"></a>
<FONT color="green">234</FONT>         * Returns the current state estimation vector.<a name="line.234"></a>
<FONT color="green">235</FONT>         *<a name="line.235"></a>
<FONT color="green">236</FONT>         * @return the state estimation vector<a name="line.236"></a>
<FONT color="green">237</FONT>         */<a name="line.237"></a>
<FONT color="green">238</FONT>        public double[] getStateEstimation() {<a name="line.238"></a>
<FONT color="green">239</FONT>            return stateEstimation.toArray();<a name="line.239"></a>
<FONT color="green">240</FONT>        }<a name="line.240"></a>
<FONT color="green">241</FONT>    <a name="line.241"></a>
<FONT color="green">242</FONT>        /**<a name="line.242"></a>
<FONT color="green">243</FONT>         * Returns a copy of the current state estimation vector.<a name="line.243"></a>
<FONT color="green">244</FONT>         *<a name="line.244"></a>
<FONT color="green">245</FONT>         * @return the state estimation vector<a name="line.245"></a>
<FONT color="green">246</FONT>         */<a name="line.246"></a>
<FONT color="green">247</FONT>        public RealVector getStateEstimationVector() {<a name="line.247"></a>
<FONT color="green">248</FONT>            return stateEstimation.copy();<a name="line.248"></a>
<FONT color="green">249</FONT>        }<a name="line.249"></a>
<FONT color="green">250</FONT>    <a name="line.250"></a>
<FONT color="green">251</FONT>        /**<a name="line.251"></a>
<FONT color="green">252</FONT>         * Returns the current error covariance matrix.<a name="line.252"></a>
<FONT color="green">253</FONT>         *<a name="line.253"></a>
<FONT color="green">254</FONT>         * @return the error covariance matrix<a name="line.254"></a>
<FONT color="green">255</FONT>         */<a name="line.255"></a>
<FONT color="green">256</FONT>        public double[][] getErrorCovariance() {<a name="line.256"></a>
<FONT color="green">257</FONT>            return errorCovariance.getData();<a name="line.257"></a>
<FONT color="green">258</FONT>        }<a name="line.258"></a>
<FONT color="green">259</FONT>    <a name="line.259"></a>
<FONT color="green">260</FONT>        /**<a name="line.260"></a>
<FONT color="green">261</FONT>         * Returns a copy of the current error covariance matrix.<a name="line.261"></a>
<FONT color="green">262</FONT>         *<a name="line.262"></a>
<FONT color="green">263</FONT>         * @return the error covariance matrix<a name="line.263"></a>
<FONT color="green">264</FONT>         */<a name="line.264"></a>
<FONT color="green">265</FONT>        public RealMatrix getErrorCovarianceMatrix() {<a name="line.265"></a>
<FONT color="green">266</FONT>            return errorCovariance.copy();<a name="line.266"></a>
<FONT color="green">267</FONT>        }<a name="line.267"></a>
<FONT color="green">268</FONT>    <a name="line.268"></a>
<FONT color="green">269</FONT>        /**<a name="line.269"></a>
<FONT color="green">270</FONT>         * Predict the internal state estimation one time step ahead.<a name="line.270"></a>
<FONT color="green">271</FONT>         */<a name="line.271"></a>
<FONT color="green">272</FONT>        public void predict() {<a name="line.272"></a>
<FONT color="green">273</FONT>            predict((RealVector) null);<a name="line.273"></a>
<FONT color="green">274</FONT>        }<a name="line.274"></a>
<FONT color="green">275</FONT>    <a name="line.275"></a>
<FONT color="green">276</FONT>        /**<a name="line.276"></a>
<FONT color="green">277</FONT>         * Predict the internal state estimation one time step ahead.<a name="line.277"></a>
<FONT color="green">278</FONT>         *<a name="line.278"></a>
<FONT color="green">279</FONT>         * @param u<a name="line.279"></a>
<FONT color="green">280</FONT>         *            the control vector<a name="line.280"></a>
<FONT color="green">281</FONT>         * @throws DimensionMismatchException<a name="line.281"></a>
<FONT color="green">282</FONT>         *             if the dimension of the control vector does not fit<a name="line.282"></a>
<FONT color="green">283</FONT>         */<a name="line.283"></a>
<FONT color="green">284</FONT>        public void predict(final double[] u) throws DimensionMismatchException {<a name="line.284"></a>
<FONT color="green">285</FONT>            predict(new ArrayRealVector(u));<a name="line.285"></a>
<FONT color="green">286</FONT>        }<a name="line.286"></a>
<FONT color="green">287</FONT>    <a name="line.287"></a>
<FONT color="green">288</FONT>        /**<a name="line.288"></a>
<FONT color="green">289</FONT>         * Predict the internal state estimation one time step ahead.<a name="line.289"></a>
<FONT color="green">290</FONT>         *<a name="line.290"></a>
<FONT color="green">291</FONT>         * @param u<a name="line.291"></a>
<FONT color="green">292</FONT>         *            the control vector<a name="line.292"></a>
<FONT color="green">293</FONT>         * @throws DimensionMismatchException<a name="line.293"></a>
<FONT color="green">294</FONT>         *             if the dimension of the control vector does not match<a name="line.294"></a>
<FONT color="green">295</FONT>         */<a name="line.295"></a>
<FONT color="green">296</FONT>        public void predict(final RealVector u) throws DimensionMismatchException {<a name="line.296"></a>
<FONT color="green">297</FONT>            // sanity checks<a name="line.297"></a>
<FONT color="green">298</FONT>            if (u != null &amp;&amp;<a name="line.298"></a>
<FONT color="green">299</FONT>                u.getDimension() != controlMatrix.getColumnDimension()) {<a name="line.299"></a>
<FONT color="green">300</FONT>                throw new DimensionMismatchException(u.getDimension(),<a name="line.300"></a>
<FONT color="green">301</FONT>                                                     controlMatrix.getColumnDimension());<a name="line.301"></a>
<FONT color="green">302</FONT>            }<a name="line.302"></a>
<FONT color="green">303</FONT>    <a name="line.303"></a>
<FONT color="green">304</FONT>            // project the state estimation ahead (a priori state)<a name="line.304"></a>
<FONT color="green">305</FONT>            // xHat(k)- = A * xHat(k-1) + B * u(k-1)<a name="line.305"></a>
<FONT color="green">306</FONT>            stateEstimation = transitionMatrix.operate(stateEstimation);<a name="line.306"></a>
<FONT color="green">307</FONT>    <a name="line.307"></a>
<FONT color="green">308</FONT>            // add control input if it is available<a name="line.308"></a>
<FONT color="green">309</FONT>            if (u != null) {<a name="line.309"></a>
<FONT color="green">310</FONT>                stateEstimation = stateEstimation.add(controlMatrix.operate(u));<a name="line.310"></a>
<FONT color="green">311</FONT>            }<a name="line.311"></a>
<FONT color="green">312</FONT>    <a name="line.312"></a>
<FONT color="green">313</FONT>            // project the error covariance ahead<a name="line.313"></a>
<FONT color="green">314</FONT>            // P(k)- = A * P(k-1) * A' + Q<a name="line.314"></a>
<FONT color="green">315</FONT>            errorCovariance = transitionMatrix.multiply(errorCovariance)<a name="line.315"></a>
<FONT color="green">316</FONT>                    .multiply(transitionMatrixT)<a name="line.316"></a>
<FONT color="green">317</FONT>                    .add(processModel.getProcessNoise());<a name="line.317"></a>
<FONT color="green">318</FONT>        }<a name="line.318"></a>
<FONT color="green">319</FONT>    <a name="line.319"></a>
<FONT color="green">320</FONT>        /**<a name="line.320"></a>
<FONT color="green">321</FONT>         * Correct the current state estimate with an actual measurement.<a name="line.321"></a>
<FONT color="green">322</FONT>         *<a name="line.322"></a>
<FONT color="green">323</FONT>         * @param z<a name="line.323"></a>
<FONT color="green">324</FONT>         *            the measurement vector<a name="line.324"></a>
<FONT color="green">325</FONT>         * @throws NullArgumentException<a name="line.325"></a>
<FONT color="green">326</FONT>         *             if the measurement vector is {@code null}<a name="line.326"></a>
<FONT color="green">327</FONT>         * @throws DimensionMismatchException<a name="line.327"></a>
<FONT color="green">328</FONT>         *             if the dimension of the measurement vector does not fit<a name="line.328"></a>
<FONT color="green">329</FONT>         * @throws SingularMatrixException<a name="line.329"></a>
<FONT color="green">330</FONT>         *             if the covariance matrix could not be inverted<a name="line.330"></a>
<FONT color="green">331</FONT>         */<a name="line.331"></a>
<FONT color="green">332</FONT>        public void correct(final double[] z)<a name="line.332"></a>
<FONT color="green">333</FONT>                throws NullArgumentException, DimensionMismatchException, SingularMatrixException {<a name="line.333"></a>
<FONT color="green">334</FONT>            correct(new ArrayRealVector(z));<a name="line.334"></a>
<FONT color="green">335</FONT>        }<a name="line.335"></a>
<FONT color="green">336</FONT>    <a name="line.336"></a>
<FONT color="green">337</FONT>        /**<a name="line.337"></a>
<FONT color="green">338</FONT>         * Correct the current state estimate with an actual measurement.<a name="line.338"></a>
<FONT color="green">339</FONT>         *<a name="line.339"></a>
<FONT color="green">340</FONT>         * @param z<a name="line.340"></a>
<FONT color="green">341</FONT>         *            the measurement vector<a name="line.341"></a>
<FONT color="green">342</FONT>         * @throws NullArgumentException<a name="line.342"></a>
<FONT color="green">343</FONT>         *             if the measurement vector is {@code null}<a name="line.343"></a>
<FONT color="green">344</FONT>         * @throws DimensionMismatchException<a name="line.344"></a>
<FONT color="green">345</FONT>         *             if the dimension of the measurement vector does not fit<a name="line.345"></a>
<FONT color="green">346</FONT>         * @throws SingularMatrixException<a name="line.346"></a>
<FONT color="green">347</FONT>         *             if the covariance matrix could not be inverted<a name="line.347"></a>
<FONT color="green">348</FONT>         */<a name="line.348"></a>
<FONT color="green">349</FONT>        public void correct(final RealVector z)<a name="line.349"></a>
<FONT color="green">350</FONT>                throws NullArgumentException, DimensionMismatchException, SingularMatrixException {<a name="line.350"></a>
<FONT color="green">351</FONT>    <a name="line.351"></a>
<FONT color="green">352</FONT>            // sanity checks<a name="line.352"></a>
<FONT color="green">353</FONT>            MathUtils.checkNotNull(z);<a name="line.353"></a>
<FONT color="green">354</FONT>            if (z.getDimension() != measurementMatrix.getRowDimension()) {<a name="line.354"></a>
<FONT color="green">355</FONT>                throw new DimensionMismatchException(z.getDimension(),<a name="line.355"></a>
<FONT color="green">356</FONT>                                                     measurementMatrix.getRowDimension());<a name="line.356"></a>
<FONT color="green">357</FONT>            }<a name="line.357"></a>
<FONT color="green">358</FONT>    <a name="line.358"></a>
<FONT color="green">359</FONT>            // S = H * P(k) - * H' + R<a name="line.359"></a>
<FONT color="green">360</FONT>            RealMatrix s = measurementMatrix.multiply(errorCovariance)<a name="line.360"></a>
<FONT color="green">361</FONT>                .multiply(measurementMatrixT)<a name="line.361"></a>
<FONT color="green">362</FONT>                .add(measurementModel.getMeasurementNoise());<a name="line.362"></a>
<FONT color="green">363</FONT>    <a name="line.363"></a>
<FONT color="green">364</FONT>            // invert S<a name="line.364"></a>
<FONT color="green">365</FONT>            // as the error covariance matrix is a symmetric positive<a name="line.365"></a>
<FONT color="green">366</FONT>            // semi-definite matrix, we can use the cholesky decomposition<a name="line.366"></a>
<FONT color="green">367</FONT>            DecompositionSolver solver = new CholeskyDecomposition(s).getSolver();<a name="line.367"></a>
<FONT color="green">368</FONT>            RealMatrix invertedS = solver.getInverse();<a name="line.368"></a>
<FONT color="green">369</FONT>    <a name="line.369"></a>
<FONT color="green">370</FONT>            // Inn = z(k) - H * xHat(k)-<a name="line.370"></a>
<FONT color="green">371</FONT>            RealVector innovation = z.subtract(measurementMatrix.operate(stateEstimation));<a name="line.371"></a>
<FONT color="green">372</FONT>    <a name="line.372"></a>
<FONT color="green">373</FONT>            // calculate gain matrix<a name="line.373"></a>
<FONT color="green">374</FONT>            // K(k) = P(k)- * H' * (H * P(k)- * H' + R)^-1<a name="line.374"></a>
<FONT color="green">375</FONT>            // K(k) = P(k)- * H' * S^-1<a name="line.375"></a>
<FONT color="green">376</FONT>            RealMatrix kalmanGain = errorCovariance.multiply(measurementMatrixT).multiply(invertedS);<a name="line.376"></a>
<FONT color="green">377</FONT>    <a name="line.377"></a>
<FONT color="green">378</FONT>            // update estimate with measurement z(k)<a name="line.378"></a>
<FONT color="green">379</FONT>            // xHat(k) = xHat(k)- + K * Inn<a name="line.379"></a>
<FONT color="green">380</FONT>            stateEstimation = stateEstimation.add(kalmanGain.operate(innovation));<a name="line.380"></a>
<FONT color="green">381</FONT>    <a name="line.381"></a>
<FONT color="green">382</FONT>            // update covariance of prediction error<a name="line.382"></a>
<FONT color="green">383</FONT>            // P(k) = (I - K * H) * P(k)-<a name="line.383"></a>
<FONT color="green">384</FONT>            RealMatrix identity = MatrixUtils.createRealIdentityMatrix(kalmanGain.getRowDimension());<a name="line.384"></a>
<FONT color="green">385</FONT>            errorCovariance = identity.subtract(kalmanGain.multiply(measurementMatrix)).multiply(errorCovariance);<a name="line.385"></a>
<FONT color="green">386</FONT>        }<a name="line.386"></a>
<FONT color="green">387</FONT>    }<a name="line.387"></a>




























































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